Hearing the music makes patterns easier to understand and predict in general, but isn't necessary to read them.

In general accuracy, the visual cue is the most important part, though it's hard to prove. In KSM, you can test this by going to config.ini and changing "inputdelay" to 0 and putting the value it had to "globaloffset". KSM is weird: the global offset you change in the game doesn't offset the audio, but adds delay to your input when a negative value is used (like in 90% cases is needed). This means that the visual timing of a button press is not at the scan line but a little before it. When you use "globaloffset" instead of "inputdelay", the actual button press will happen when the note is closer to the scan line. The variable "globaloffset" can't be changed in the game at all, and changing it in the config messes up laser slam sound timing. So, if you test this, do it with an SDVX chart that has laser sounds within the audio.

When you test this, you'll notice that even though the sync of audio and timing stays the same, it will feel really weird and you'll become more much inaccurate because of having not got used to it.

But even though visual cue is important, for the most extreme accuracy, the music is the icing on the cake. But it only works when the offset is perfect (usually it isn't, and setting it perfectly is another difficult art. You can change and save it to chart in KSM by ctrl+alt(+shift)+left/right arrows while in game.) With some lvl13 songs (easy but dense enough for consistent beat), I have 20-50% Perfect rate (no nears). For that accuracy, audio is completely essential, I couldn't do nowhere as well without the it. It also depends a lot on the song production like sync of the instruments for clear beat. Instrument sync is a delicate thing and about milliseconds that pretty much can't even be heard, but it affects your play. It's just that in some songs I get more perfects than in others regardless of difficulty, but electronic songs like Indomitable spirit are generally better than a rock song where the guitar part is played by human.